OCR MEI Further Pure Core 2019 June — Question 14

Exam BoardOCR MEI
ModuleFurther Pure Core (Further Pure Core)
Year2019
SessionJune
Topic3x3 Matrices

14 Three planes have equations $$\begin{aligned} - x + a y & = 2
2 x + 3 y + z & = - 3
x + b y + z & = c \end{aligned}$$ where \(a\), \(b\) and \(c\) are constants.
  1. In the case where the planes do not intersect at a unique point,
    1. find \(b\) in terms of \(a\),
    2. find the value of \(c\) for which the planes form a sheaf.
  2. In the case where \(b = a\) and \(c = 1\), find the coordinates of the point of intersection of the planes in terms of \(a\).